let p, q, s be Element of HP-WFF ; :: thesis: ((p '&' s) => q) => ((p '&' s) => (q '&' s)) in HP_TAUT
set P = p '&' s;
A1: ((p '&' s) => q) => (((p '&' s) => s) => ((p '&' s) => (q '&' s))) in HP_TAUT by Th35;
(p '&' s) => s in HP_TAUT by Def10;
hence ((p '&' s) => q) => ((p '&' s) => (q '&' s)) in HP_TAUT by A1, Th29; :: thesis: verum